Genetic algorithm (GA) is a type of widely used and well studied heuristic algorithms for the TSP. Many studies have made efforts to design crossover operators appropriate to the TSP ([1]} [1]}, [3]} [3]}, [5]} [5]}, [7]} [7]}, [9]}, [10]} [10]}, [12]} [12]}, [14]} [14]}) since the performance of GAs strongly depends on the design of crossover operators. Among these GAs, the EAX-GA ([7]} [7]}) and its improved versions ([14]} [14]}, [9]} [9]}) are the best performing algorithms, which generate offspring solutions by combining edges from the two parent solutions and adding relatively few new short edges determined by a simple search procedure that is similar to the 2-opt local search. Moreover, [22]} ([22]}) proposes to use a new offspring selection operator based on the edge entropy that strongly improves the diversity of the population. The current version of EAX-GA ([9]} [9]}) is one of the most successful heuristic algorithms for solving the TSP.
